Existence and uniqueness of the Karcher mean on unital \(C^\ast\)-algebras

DOI10.1016/j.jmaa.2019.123625zbMath1477.47093arXiv1901.09776OpenAlexW2981751745MaRDI QIDQ2287221

Jimmie D. Lawson

Publication date: 20 January 2020

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.09776

zbMATH Keywords

barycenter\(C^{\ast}\)-algebraKarcher meanKarcher equation

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Convex sets and cones of operators (47L07) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (5)

Geometric means of quasi-Toeplitz matrices ⋮ Existence, uniqueness and an ODE approach to the \(L^1\)-Karcher mean ⋮ Unnamed Item ⋮ Following the Trail of the Operator Geometric Mean ⋮ Analyticity of the Karcher mean coefficient maps

Cites Work

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• Operator means of probability measures and generalized Karcher equations
• The stochastic order of probability measures on ordered metric spaces
• A Cartan-Hadamard theorem for Banach-Finsler manifolds
• Ordered probability spaces
• Karcher means and Karcher equations of positive definite operators
• Riemannian center of mass and mollifier smoothing
• Contractive barycentric map
• Symmetric spaces with convex metrics
• On Certain Contraction Mappings in a Partially Ordered Vector Space

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